Question: Simplify the following expression: $ p = \dfrac{9n + 2}{8n - 2} + \dfrac{8}{3} $
Explanation: In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{3}{3}$ $ \dfrac{9n + 2}{8n - 2} \times \dfrac{3}{3} = \dfrac{27n + 6}{24n - 6} $ Multiply the second expression by $\dfrac{8n - 2}{8n - 2}$ $ \dfrac{8}{3} \times \dfrac{8n - 2}{8n - 2} = \dfrac{64n - 16}{24n - 6} $ Therefore $ p = \dfrac{27n + 6}{24n - 6} + \dfrac{64n - 16}{24n - 6} $ Now the expressions have the same denominator we can simply add the numerators: $p = \dfrac{27n + 6 + 64n - 16}{24n - 6} $ $p = \dfrac{91n - 10}{24n - 6}$